That's precisely what these vessels need. And the Naval Strike Missile has a range out to a couple of hundred kilometers when ship launched. That is a good solution.
I've always wondered why the USN didn't use some of the space of the LCS designs to install even eight or four AShMs... surely they have the space for it, and it isn't like they haven't contracted out more complex redesigns or refits on ships before. Even if they intended for the ship to "only" do littoral missions, I wouldn't have slept well at night knowing they don't even have at least some kind of credible ship killing ability.
I suppose the big question is how much money it would take to either redesign the LCSs for such a missile load, and/or how much it would take to change the existing LCSs to accommodate such weapons. I also wonder if the inclusion of such weapons may impact the other missions the LCS was meant to do.
But even if the LCSs had to sacrifice a capability like ASW or mine hunting for those many AShMs it would still be a good trade -- they would effectively be the ultimate missile boat, with long range, endurance, impressive missile count, as well as two helicopters. Much more high intensity warfare oriented.
Edit: I just realized their independence redesign shows two 6 shot missile launchers right next to the bridge and inside the superstructure!! Gosh, I wonder if that's sensible... who came up with that particular placement., jeez.